I'll be getting the new Smash for the purposes of a party game to play with friends no matter what. However, I would like to see this game succeed on the competitive level as well. I'm sure the game will no matter what, but it would be cool to have the game still be popular competitively thirteen years after its release. I think the best way to do that is to have the engine build off of Melee's (not a direct port, obviously) seeing as Melee, at least gameplay-wise was the most universally liked. Competitive players enjoyed the technical depth, movement options, and combo potential, while everyone I know who played the game casually never had an issue with it. I was five when it came out and I had no issues with the controls whatsoever.
It would be nice to see most mechanics that have been present in most Smash games return, such as DI, SDI, teching, powershielding, crouch cancelling, autocancelling, etc. Seems like light-shielding is a lost cause at this point, unfortunately.
In terms of expanding on Melee, I would like to see directional air dodging return while adding a new mechanic that obsoletes the need for wavedashing (at least for most characters). I'm picturing some sort of back walk feature, allowing a character to move backwards while still facing in one direction, kind of like traditional fighting games. Perhaps it could be done by holding R and moving the joystick. Seeing as L and R do the same thing in Smash this shouldn't be a big loss, and players who used to shield with R could choose to map it that way in the settings. While back walking, the character can perform tilts and jabs and anything else that can be done from a normal walk. In a sense, it is simply a more intuitive and natural looking wavedash.
As for L-Cancelling, they could probably just bring it back with no fuss, but it would be nice to see it expanded upon a bit as well. I would like there to be a reason to not always L-Cancel an aerial, perhaps during landing lag from an aerial you recieve less knockback from attacks in a vein similar to crouch cancelling, while L-Cancelled aerials suffer normal or perhaps increased knockback. This would create a dynamic where you want to L-Cancel when on the offensive and not L-Cancel when on the defensive. This would allow L-Cancelling to lose the stigma of being an arbitrary tech barrier.
However, it is looking like the new Smash will be it's own beast entirely, which is fine. I want to reserve judgement until we have the final game and have analyzed it, and I'm sure the game will have a competitive scene that goes strong at least for a while. However, I would like to see the game have a lasting appeal competitively like Melee does, with a meta that is still active and changing and even growing well over a decade after release. I think the best way to do this is to expand upon Melee's mechanics which clearly have stood the test of time.